CN103777518B - Satellite navigation time service system and method based on the method for least square improved - Google Patents

Abstract

nullThe present invention relates to satellite navigation time service system and method based on the method for least square improved，System includes base band demodulating module、Positioning calculation module、Least square time service module、Local clock and second signal generator，Base band demodulating part by the moonscope amount obtained and loop integral energy input to positioning calculation part，Thus obtain positional information and the clock correction information of receiver，Utilize method of least square will to be fitted time during this locality with system afterwards，When obtaining corresponding local of whole moment second during next system，Eliminate a part of effect of noise，Complete high accuracy time service，By making least square fitting to during this locality with orthogonal polynomial model during system，Reduce the shake of second signal generator，Improve time service precision，Caused more greatly degeneration and the problem of coefficient solution extremely unstable of finding the inverse matrix when solving general polynomial matching by exponent number simultaneously.

Description

Satellite navigation time service system and method based on the method for least square improved

Technical field

The present invention relates to field of satellite navigation, specially relate to a kind of satellite navigation based on the method for least square improved and award Time system and method.

Background technology

In recent years, along with the development of satellite navigation system, the application of Technique of Satellite Navigation and Positioning is increasingly wider, Being widely used in many industries such as communication, electric power, traffic, satellite navigation time service service has precision height, wide coverage, cost The feature such as cheap, has become as one critical function of satellite navigation system, provides Perfect Time service for industry-by-industry.

The clocking error of local receiver, while realizing location and constant speed function, can be believed by satellite navigation system Breath resolves in the lump.In general, according to the principle of satellite navigation location, the satellite that observation simultaneously is more than four, it is possible to Realize location, and receiver clock-offsets can be calculated.Simultaneously from the definition of time service, GPS receiver is utilized to carry out time service main It is to obtain current moment, carries out the code acquisition of satellite by receiver, follow the tracks of, demodulate navigation message, by calculating Clock correction can obtain the current moment, complete time service.

But, directly utilized clock correction information in the past and second signal be corrected error relatively greatly, and Crystal Oscillator Errors also can carry The clocking error come, it is therefore desirable to technical staff innovates from the circuit and processing method of satellite navigation time service system and changes Come in solve these not enough.

Summary of the invention

The purpose of the present invention is aiming at directly utilizing clock correction information and second signal is corrected error relatively greatly, and crystal oscillator The shortcoming of the clocking error that error is brought, it is provided that a kind of satellite navigation time service system based on the method for least square improved and side Method, by establishing orthogonal polynomial model to during the system of a period of time Continuous Observation with the time series constituted time local, Carry out least square fitting such that it is able to forecast when directly utilizing model to this locality, reduce the shake of clock, have simultaneously Effect solves the ill-condition matrix problem that general polynomial matching exists.

The technical scheme is that

A kind of satellite navigation time service system based on method of least square, it is characterised in that include base band demodulating module, location Resolve module, least square time service module, local clock and second signal generator；

Base band demodulating module, by the moonscope amount received and loop integral energy, passes to positioning calculation module, Positioning calculation module resolves the receiver clock-offsets information that obtains and tries to achieve system time, least square time service module to during system with Orthogonal polynomial model is used to carry out least square fitting time local, in the second when calculating corresponding local of whole moment second during system Exporting in signal generator, obtain pps pulse per second signal, on the one hand local clock works for base band demodulating module, on the one hand control Second signal generator processed started to reset counting in whole moment second, and wherein, least square time service module is by positioning calculation module, minimum Two take advantage of wave filter, local clock and second signal generator to connect and compose.

Utilize the method that described a kind of satellite navigation time service system based on method of least square realizes satellite navigation time service, its It is characterised by, described least square time service module carries out a young waiter in a wineshop or an inn to during system with using orthogonal polynomial model time local Taking advantage of matching, it is achieved least square time service, described method comprises the steps:

Step 1: positioning calculation module, according to the moonscope amount received and loop integral energy information, calculates and connects Receipts machine clock correction information, thus when obtaining with this localityDuring corresponding system；

Step 2: carrying out least square fitting to time during this locality with system, process is as follows:

The most all there is polynomial feature due to time series, when fitting of a polynomial model therefore can be used to come this locality It is fitted during with system；When assuming this localityDuring corresponding systemCan use following polynomial repressentation:

(1)

Wherein,For multinomial coefficient, k is exponent number；

Observation station when assuming to take one group of this localityDuring corresponding system it is, corresponding clock Difference is, then equation is represented by:

Then have:

Above formula is write as matrix form:

Wherein,It is vectorial for clock correction,For vectorial during system,For coefficient vector corresponding with time local during system, For vectorial, then during this locality:

,,,

Solve can obtain according to method of least square:

Polynomial coefficient can be tried to achieve by above formula, then bring this polynomial coefficient into multinomial model, the most available Required multinomial model；

Found that used multinomial does not determine polynomial exponent number by series of computation, for during this locality and system Time fitting of a polynomial, exponent number is the biggest, the most accurate to frequency drift correction, but amount of calculation is relatively big, and matrixClose to degenerating, it is The solution of numberAlso extremely unstable；

Step 3: with multinomial model time local when utilizing the system obtained, tries to achieve during system corresponding to whole moment second Time local, second signal generator obtains information output pps pulse per second signal during this locality, completes high accuracy time service；

Described least square time service module carries out least square to during system with using orthogonal polynomial model time local Matching, uses orthogonal polynomial model matching to avoid the inversion process of matrix, and calculating process is simple, and orthogonal polynomial ratio General polynomial is more stable, and easily quickly determines polynomial exponent number, and process is as follows:

For formula (1), represent with recurrence formula, it may be assumed that

() (2)

Can be to be written as form:

(3)

Wherein,Be respectively t once, secondary ..., k order polynomial,It is that some are optional Constant, by (1) formulaUse respectivelyReplace, can obtain after arranging:

(4)

WhereinFor multinomial coefficient, k is exponent number；

Substantially (1) as broad as long with (4) formula, the most pro forma difference, if handleRegard as New independent variable,In the moment, have (4) formula turns to least squares equation:

(5)

Wherein:

(6)

ForFamily of functions, can select coefficientMake function Race meets orthogonality condition, it may be assumed that

(7)

Then:

(8)

Then equation (5) can be write as:

(9)

Solve equation and can obtain:

(10)

Use orthogonal polynomialLinear combination make least square curve fitting, as long as according to formula (2) and (7) progressively ObtainWhile, calculate coefficient accordingly according to formula (10), and progressivelyIt is added toIn go last i.e. Can obtain the matched curve of orthogonal polynomial model:。

Beneficial effect

Present invention design satellite navigation time service system based on the method for least square improved, by time during this locality with system Orthogonal polynomial model make least square fitting, reduce the shake of second signal generator, improve time service precision, solve simultaneously Determined general polynomial matching time caused more greatly the degeneration of finding the inverse matrix by exponent number, thus cause asking of coefficient solution extremely unstable Topic.

Accompanying drawing explanation

Fig. 1 is the satellite navigation time service system block diagram based on the method for least square improved of the present invention.

Fig. 2 is least square time service module block diagram in the present invention.

In figure: in figure: 01. positioning calculation module, 02. base band demodulating module, 03. local clock, 04. least square Time service module, 05. second signal generator.

Detailed description of the invention

Below in conjunction with specific embodiment the present invention described:

The specific embodiments figure of the present embodiment as shown in Figure 1 and Figure 2, award by a kind of satellite navigation based on method of least square Time system, including base band demodulating module 02, positioning calculation module 01, least square time service module 04, local clock 03 and second believe Number generator 05.Base band demodulating module 02, by the moonscope amount received and loop integral energy, passes to positioning calculation Module 01, positioning calculation module 01 tries to achieve system time, least square time service module with resolving the receiver clock-offsets information obtained Carry out least square fitting with using orthogonal polynomial model time local during 04 pair of system, calculate whole moment second during system corresponding Local time export in second signal generator, obtain pps pulse per second signal, local clock 03 1 aspect is base band demodulating mould Block works, and on the one hand controls second signal generator and starts to reset counting in whole moment second.

Least square time service module 04 is main by positioning calculation module, least square filter, local clock and second signal Generator connects and composes.

According to the above description, the solution of the present invention can be realized in conjunction with art technology.

Claims (2)

1. a satellite navigation time service system based on method of least square, it is characterised in that include that base band demodulating module, location solve Calculate module, least square time service module, local clock and second signal generator；

Base band demodulating module, by the moonscope amount received and loop integral energy, passes to positioning calculation module, location Resolving module resolves the receiver clock-offsets information obtained and tries to achieve system time, and least square time service module is to during system and this locality Shi Caiyong orthogonal polynomial model carries out least square fitting, at second signal when calculating corresponding local of whole moment second during system Exporting in generator, obtain pps pulse per second signal, on the one hand local clock works for base band demodulating module, on the one hand controls the second Signal generator started to reset counting in whole moment second, and wherein, least square time service module is by positioning calculation module, least square Wave filter, local clock and second signal generator connect and compose.

2. utilize a kind of satellite navigation time service system based on method of least square described in claim 1 to realize satellite navigation time service Method, it is characterised in that entered with using orthogonal polynomial model time local during system by described least square time service module Row least square fitting, it is achieved least square time service, described method comprises the steps:

Step 1: positioning calculation module, according to the moonscope amount received and loop integral energy information, calculates receiver Clock correction information, thus obtain x (t) during the system corresponding with t time local；

Step 2: carrying out least square fitting to time during this locality with system, process is as follows:

The most all there is polynomial feature due to time series, therefore can use fitting of a polynomial model to during this locality be It is fitted during system；When assuming this locality, during system corresponding to t, x (t) can use following polynomial repressentation:

X (t)=a₀+a₁t+a₂t²+…+a_kt^k (1)

Wherein, a₀,a₁,a₂,…a_kFor multinomial coefficient, k is exponent number；

Observation station t when assuming to take one group of this locality₁,t₂,…,t_mIt is x (t during corresponding system₁),x(t₂),…,x(t_m), accordingly Clock correction is v₁,v₂,…,v_m, then equation is represented by:

$\begin{array}{c}x\left(t_1\right)+v_1=a_0+a_1{t}_1+a_2{t_1}^2+\mathrm{...}+a_k{t_1}^k\\ x\left(t_2\right)+v_2=a_0+a_1{t}_2+a_2{t_2}^2+\mathrm{...}+a_k{t_2}^k\\ .\\ .\\ .\\ x\left(t_m\right)+v_m=a_0+a_1{t}_m+a_2{t_m}^2+\mathrm{...}+a_k{t_m}^k\end{array}$

Then have:

$\begin{array}{c}{v}_1=a_0+a_1{t}_1+a_2{t_1}^2+\mathrm{...}+a_k{t_1}^k-x\left(t_1\right)\\ v_2=a_0+a_1{t}_2+a_2{t_2}^2+\mathrm{...}+a_k{t_2}^k-x\left(t_2\right)\\ .\\ .\\ .\\ v_m=a_0+a_1{t}_m+a_2{t_m}^2+\mathrm{...}+a_k{t_m}^k-x\left(t_m\right)\end{array}$

Above formula is write as matrix form:

V=Aa-X

Wherein, V is clock correction vector, vector when X is system, coefficient vector corresponding with time local when a is system, when A is local Vector, then:

$V=\left[\begin{array}{c}{v}_1\\ v_2\\ .\\ .\\ .\\ v_m\end{array}\right],X=\left[\begin{array}{c}x\left(t_1\right)\\ x\left(t_2\right)\\ .\\ .\\ .\\ x\left(t_m\right)\end{array}\right],a=\left[\begin{array}{c}{a}_0\\ a_1\\ .\\ .\\ .\\ a_m\end{array}\right],A=\left[\begin{array}{ccccc}1& t_1& t_1^2& \mathrm{...}& t_1^k\\ 1& t_2& t_2^2& \mathrm{...}& t_2^k\\ .& .& .& .& .\\ .& .& .& .& .\\ .& .& .& .& .\\ 1& t_m& t_m^2& \mathrm{...}& t_m^k\end{array}\right]$

Solve can obtain according to method of least square:

(A^TA) a=A^TX

A=(A^TA)^-1A^TX

Polynomial coefficient can be tried to achieve by above formula, then bring this polynomial coefficient into multinomial model, i.e. available required The multinomial model wanted；

Found that used multinomial does not determine polynomial exponent number by series of computation, for during this locality with system time Fitting of a polynomial, exponent number is the biggest, the most accurate to frequency drift correction, but amount of calculation is relatively big, and matrix A^TA is close to degenerate, coefficient Solve a also extremely unstable；

Step 3: with multinomial model time local during the system that utilization obtains, try to achieve this locality corresponding to whole moment second during system Time, second signal generator obtains information output pps pulse per second signal during this locality, completes high accuracy time service；

Described least square time service module carries out least square fitting to during system with using orthogonal polynomial model time local, Using orthogonal polynomial model matching to avoid the inversion process of matrix, calculating process is simple, and orthogonal polynomial ratio is general Multinomial is more stable, and easily quickly determines polynomial exponent number, and process is as follows:

For formula (1), represent with recurrence formulaThat is:

Can be to be written as form:

Wherein,Be respectively t once, secondary ..., k order polynomial, β_i,jIt is that some are the most normal Number, by the t in (1) formula^kUse respectivelyReplace, can obtain after arranging:

Wherein b₀,b₁,b₂,…b_kFor multinomial coefficient, k is exponent number；

Substantially (1) as broad as long with (4) formula, the most pro forma difference, if handleRegard new as Independent variable, at t₁,…,t_mIn the moment, have (4) formula turns to least squares equation:

Wherein:

Wherein L is intermediate parameters；

ForFamily of functions, can select factor beta_1,0,β_2,1,β_2,0,...,β_k,k-1,...,β_k,0Make function Race meets orthogonality condition, it may be assumed that

Then:

Then equation (5) can be write as:

Solve equation and can obtain:

Use orthogonal polynomialLinear combination make least square curve fitting, as long as progressively obtaining according to formula (2) and (7)While, calculate coefficient b accordingly according to formula (10)_i, and progressivelyIt is added in x (t) to go finally The matched curve of orthogonal polynomial model: